Chapel With Polyhedral Transformation Using Autotuning TuowenZhao - - PowerPoint PPT Presentation

Chapel With Polyhedral Transformation Using Autotuning

TuowenZhao and Mary Hall

The 3rd Annual Chapel Implementers and Users Workshop,2016

Loop Transformation

• Manipulation of loop nest
• Structure
• Schedule
• Prior work: manually apply loop transformations in

Chapel

• I. J. Bertolacci et al. Parameterized diamond tiling for

stencil computations with Chapel parallel iterators. ICS 2015

• A. Sharma et al. Affine loop optimization based on

modulo unrolling in Chapel. PGAS 2014

• We: Automatically applied loop transformations

using recipes from script which enables integration with autotuning framework

Contribution

• Uses C code to capture sequential computation
• Generates Chapel programs by composing

polyhedral transformations on the sequential computation and mapping from iteration spaces to Chapel domains and iterator

• Demonstrates with a simple example in Chapel the

benefits of applying such transformations in conjunction with autotuning

Chapel Language

proc mm(A:[]real,B:[]real, an:int,ambn:int,bm:int){ const D = {0..an-1, 0..bm-1}; // Domain var C : [D] real; // Domain mapped array forall (i,j) in D do { // Iterator C[i,j] = 0; for k in {0..ambn-1} do C[i, j] += A[i, k] * B[k,j]; } return C; }

Polyhedral Framework

• Iteration Spaces
• A set of iteration vectors represented as integer tuples
• Direct mapping from Chapel domain
• Transformation done by linear mapping
• Affine loop bounds, conditional expressions, array

subscripts

Dependence analysis

• Ensure validity of transformation and correctness of

program

• Have to know the order of references to each array

elements

• Cannot be applied to Chapel iterator without

programmer intervention or runtime information

CHiLL

• Composable High-Level Loop transformation

framework

• A polyhedral transformation and code generation

framework

• Relies on autotuning to generate highly-tuned

implementations for a specific target architecture

• Uses a transformation recipe to express optimization

strategy (recipe may be generated by a compiler)

Architecture Overview

Experiment – matrix multiply

• Input in C

for(i = 0; i < an; i++) for(j = 0; j < bm; j++) { C[i][j]=0.0f; for(n = 0; n < ambn; n++) C[i][j] += A[i][n] * B[n][j]; }

• Tile sizes {8; 16; 32; 64;

128; 256}

• Distribution of the

initialization code

• Tile sizes
• Chapel’s configuration

variable

• Literal constant
• Intel Haswell i7-4790K
• 16GB DDR3 RAM

Result

Stencil Computations

• Operations on structured grids
• MiniGMG
• Geometric multigrid benchmark
• Uses stencil computations extensively especially in

smooth and residual operators

• CHiLL on MiniGMG
• P. Basu (2015) Compiler Optimizations and Autotuning

for Stencils and Geometric Multigrid. PhD thesis. University of Utah

Stencil Optimizations

• Communication avoiding optimizations
• Wavefront(loop fusing)
• Deeper ghost zones with redundant computation

User-defined library

• StencilDist library
• Problems
• Can’t guarantee correctness(dependence)
• Handwrite optimized code
• Generality concern

Multi-locale Stencil

Multi-locale Stencil

Multi-locale Stencil

• Programmer writes simple serial code fragments
• Recipes provided by programmer or generated by

autotuner

• Behind-the-scene generation of distributed

computation and distributed data

• Produce fine-tuned code without programmer’s

rewriting

Conclusion

• Integrating Chapel with CHiLL
• Instantly enables a lot of different optimization

techniques that can be composed in complex sequences

• Autotuningcan be used to find the best performing

combination of transformations under target architecture

Future work

• Expanding the domain of autotuning by generating

and tuning domain maps and iterators

• Relaxing the transformation requirements by

generalize to non-affine loop bounds and subscripts that employ indirection through an index array

Questions?